It can take some time to kill grass depending on what kind of grass you have and how much water you are dumping. If you like your grass, don't dump saltwater on it.

You won't hurt a septic system. The system processes 1000s of gallons of water and 10-50 gallons of saltwater a month won't cause any problem. Many more nasty things get pumped into your septic system.

I put all my water down the drain or down the driveway depending on where I am moving the water from. Oh, and I rarely do a water change. Even on my 20 gallon.